The Continuing Power of Hidden Polygons in the Banded Crop Circles of 2017
A research article by Jack Sullivan.
This is essentially an update of my article of the 7th of November 2015 published in the Research Pages of the Crop Circle Connector website. That article is titled; “Crop Circles and the Prevalence of Polygons”. It discloses facts and evidence of the presence of hidden polygon structures in over thirty examples of banded crop formations dating back to 1960, examines the geometry involved and also the benefits to designers of using such structures. Their use by the creators of crop formations has continued. This year, 2017 there have been eight significant further examples demonstrating powerful logical reasons for using polygon based designs. These reasons may be seen as intended practical gifts to our human artists who use geometry in their work in whatsoever field. Each of these examples is featured with an analysis below. They are not listed in the order of the date of their appearance in the field.
Boreham Wood. Nr. Winchester 1st of July 24, 2017
This formation has two outer bands the proportions of which are determined by two hidden polygons. The outer one six sided and the secondary one seven sided. The polygons provide the division points for the seven petals and also for the central small hexagon. See the accurate replica drawing below.
This is a remarkable crop circle design since to accurately replicate it at any desired scale only three lines are essential. No physical measurements are needed. The only tools required are simple drawing instruments as commonly found in a Students Geometry Set. Compasses, a Protractor to measure the angles and a straight edged Ruler, or their equivalents dependent on the scale of your intended replica. See below
Illustration of the two fundamental Stages involved in producing an accurate Replica of the overall design.
Based on this analysis it, becomes obvious that other polygon values than the ones used could be substituted, or additional bands added using different value angles to form other polygons. These changes would enable different, may be more elaborate multi petalled designs for the central area infill. This is an example of the enduring power of polygon based geometrical design.
Battlebury Hill Nr. Winchester July 1st 2017.
Battlebury Hill Analysis Drawing.
At first sight it would appear unlikely that this formation has hidden polygons as a design basis but it is actually another clever construction which utilizes four three sided polygons to render it capable of quick and accurate replication to any desired scale without the need to rely on measurements other than the sixty degree angles. The analysis drawing shows the stages of construction after five identically sized circles 1 to 5 are drawn initially to any chosen scale, guided by horizontal and vertical centre lines. The triangular polygons govern the dimensions of the central discs in the four outer circles which in turn then govern the widths of the two circumferential bands. All other minor details can then be added to this basic construction to match the field image.
Summer Lane Broad Hinton. Wilts 28th May 2017
This small multi-banded crop circle suggests at first glance that hidden polygons are incorporated in the design. This is indeed the case and the band widths are governed by 5 hexagon polygons. There is also one large 3 sided polygon which defines the size of the central circle. The six large part-circles covering the bands may have been added after the formation was discovered because there is no relationship with the polygons, and the 6 divisions used to position them are erroneous in that they fail to fit the circumference. “To err is human” as the saying goes
The Science Space Centre. Nr. Winchester Hants.
This relatively small banded formation has a hidden cascade of 7 x four sided polygons governing the band widths, six of which are divided into decorative quadrants by having only alternating sections of laid crop. This would seem to be a simple device but it is difficult to imagine, if humans were involved, how the precisely defined lay could be achieved without error and without damaging adjacent standing crop? See the marked up ‘Connector’ aerial photograph below.
Thorn Hill 2 . East Kennet June 26 2017.
The aerial photo by Jane Barford published by ‘The Crop Circle Connector’ on the web page for this formation. has high resolution with only a little distortion and is accurate enough to allow an initial geometrical analysis to be directly applied to a print-out of her photo. This is clearly a multi banded creation. The two half band ends are truly circular and inserting Chord Lines inside them confirms that they both hold halves of perfect pentagons. See analysis replica drawing below. This is a very long (approx 200ft.) formation and to produce a perfectly accurate aerial photo would be very difficult. Thus there is some ovality of the circles which distorts the applied polygons. A true accurately drawn replica analysis using all the indicated hidden polygons became a necessity. This has revealed that the formation is a veritable feast of hidden polygons, all essential to the overall design, and again as with all the polygon structured designs found so far, enabling its logical step by step process of construction to be determined. No measurements are required other than precise installation of the polygon angles. Any replication will be true to the original design proportions irrespective of scale. This latter statement applies to any crop formation where polygons are the essential but hidden element of the structure.
Stage by stage construction. All the hidden structures are shown as broken lines.
To create a true replica at any desired scale, only three identically sized circles are required as shown.
Monarchs Way. Nr. Wooton Wawan. Warks. Aug.7 2017.
This relatively small crop formation, approximately 25 metres. diameter appears to have excrescences added by others post its original creation. I have ignored them in my analysis as being irrelevant. The Circle itself with its strange ‘spoked’ wheel centre features, despite whatever it is intended to convey, has to be genuine as proven by the two outer bands which owe their proportions to hidden polygons. See my true geometric replica below with apologies for my somewhat crude attempt at depicting the internal aspects. The two polygons, One Six sided and One Five sided again enable reproduction of the correct main proportions at any desired scale.
Bydemill Copse Nr. Hannington Wilts. August 4th 2017.
The Connector aerial photo image above has some perceptible distortion but non the less it is good enough to allow its hidden polygon structures to be clearly depicted. The design concept is very similar to the Boreham Wood formation of the 4th July. (please see above) It is of course much more elaborate with greater complexity but the same geometrical analysis applies. The polygons determine the widths and proportions of all the bands and as with other such structured creations enable perfect replication to any desired scale without the need for measurements other than the angles. The three outer bands also as at Boreham Wood, create accurate division markers for the multi petalled design of the central area which is based on the initial 12 sided polygon split into equal halves to give the 24 divisions required. The individual petal outlines are described by 24 circular arcs which have their focal points located on the inner rim of the second narrow band. I have marked the radii for two of these arcs on the above image to indicate how the whole set of 24 arcs can be formed by working from centre points at thirty degree intervals in clockwise and anti clockwise directions on this inner rim. I am sure that this formation and the other polygon structured formations could be replicated as sand circles which would be an exercise no more difficult than producing them on a drawing board, accidental errors during the process can be easily erased and correctly redrawn. However I am unable to believe that any human team could repeat the process in an arable standing crop. The marking out of construction lines which are to be invisible in the finished creation and the accurate flattening of the laid crop in the time available without error is a task beyond us and our present technology. I would love to be proved wrong, any takers out there?
Rollright Stones Nr Little Compton. Oxon August 5th 2017.
This is a further example of the basic design concept as used at Boreham Wood and Bydemill Copse, ( see above). The outer 9 sided narrow band governs the proportions of the other circular components and also determines the size of the large rectangle, the three large triangles and the 2 x sets of eight smaller triangles. The drawing was developed without the use of any measurements to a randomly selected outer diameter using only the measured angles as shown. The exercise confirmed that as with other polygon structured formations the design concept enables very accurate replication of the intended image regardless of field or camera distortions, provided only that existence of the hidden polygons is recognized.
With my earlier work on these types of banded crop formations we now have an archive of over forty such examples dating back to 1960. There are probably many more historical examples yet to be discovered perhaps so far unrecognized from other regions of the world. It is probably a certainty that as long as the crop circle phenomenon continues there are going to be many more to enlighten and amaze us in coming seasons. They will prevail until we openly accept the truth of the presence of our benevolent visitors among us.
JS. September 2017